Question

2.1.13 Find the quadratic function whose graph is shown to the right. Write the function in the form f(x) = a (x - 5)2 + kf(x)=???(Do not simplify.)

Answer 1

We are asked to find the equation (in vertex form) of the given parabolla, by using the information from its graph.

We know that the vertex is located at the top of the graph (-2, 9), and that it is a parabolla with branches pointing down (so the leading coefficient must be a negative value.

We use the vertex form of the parabola , using the coordinates of the vertex we see:

`f(x)=a(x+2)^2+9`

and proceed to determine the value of "a" by using the point we know the function is going through: (0, 5):

`\begin{gathered} f(x)=a(x+2)^2+9 \\ 5=a(0+2)^2+9 \\ 5-9=a\cdot4 \\ -4=4a \\ a=-1 \end{gathered}`

Therefore, we found the vertex form of the quadratic represented by the given graph to be:

f(x) = - (x+2)^2 + 9

`f(x)=-(x+2)^2+9`